Factor analysis - FACTORAN how to impose restrictions

I have a dataset of 17 variables and 480 observations, matrix=(480,17). I use FACTORAN to compute the maximum likelihood estimate of the factor loadings matrix with 3 common factors, lambda=(17x3) ; but i previous need to impose some restrictions on the factors of lambda. I need that: the first row is equal to [1 , 1, 0]; the 9th row equal to [1 , 0.5, 0]; the 17th row equal to [1 , 0, 0]; but i don't know how to impose these restrictions in Factoran.

Thanks for the help

Matteo

Answer 1

[arushi]

Hi Matteo,

To impose specific constraints on the factor loadings matrix when using factoran in MATLAB, you can use a workaround since factoran does not directly support constraints. You can use optimization techniques to manually adjust the factor loadings matrix to satisfy the constraints. Here's a generalguide on how to implement this using MATLAB's optimization functions:

1. Initial Factor Analysis: Perform factor analysis without constraints to get an initial estimate of the factor loadings.
2. Optimization Setup: Use MATLAB's fmincon to adjust the factor loadings matrix to satisfy the desired constraints while minimizing the discrepancy between the observed and implied covariance matrices.
3. Custom Objective Function: Create an objective function that computes the discrepancy between the implied and observed covariance matrices, subject to the constraints on specific rows of the factor loadings matrix.

Hope this helps.